Mathematics
In the given figure, D is mid-point of AB, DE//BC and DF//AC. Prove that : DE = BF.
Triangles
2 Likes
Answer
Given: ABC is triangle with D as mid-point of AB and DE//BC and DF//AC.
To Prove: DE = BF
Proof: Since D is the mid-point of AB and DE//BC, by the converse of the mid-point theorem, E is the mid-point of AC.
Thus, DE = BC ……………….(1)
Similarly, since D is the mid-point of AB and DF//AC, by the converse of the mid-point theorem, F is the mid-point of BC.
Thus, BF = BC ……………….(2)
From equations (1) and (2), we get:
⇒ DE = BF
Hence, DE = BF.
Answered By
3 Likes
Related Questions
Evaluate :
Evaluate :
State, true or false, for each of the following statements.
(i) If three angles of two triangles are equal, the triangles are congruent.
(ii) If two sides of a right triangle, containing right angle, are equal to corresponding sides of another right triangle, the triangle are congruent.
(iii) If two triangles are congruent, then the corresponding angles are equal.
(iv) If two angles and a side of one triangle are equal to two angles and a side of another triangle, the triangles are congruent.
Show that the two triangles given in the following figure are congruent.
